Question

What is quartile 1 (Q1)quartile 3 (Q3) and the IQR? Answer all three parts . 13, 23, 24, 25, 26, 26, 37, 47, 47, 48, 50

Answer 1

Quartile 1 (Q1) = 24

Quartile 2 (Q2) = 47

IQR = 23

Explanation:

Given:

The set of data are:

13, 23, 24, 25, 26, 26, 37, 47, 47, 48, 50

The data are in increasing order. The number terms are,
`n = 11`.

Therefore, the middle term =
`(n+1)/(2)=(11+1)/(2)=6^(th)\ term`

So, the median = 26

Now, the median divides the set of data into two parts. The median of first part is the quartile 1 and the median of second part is quartile 2.

So, the first part has the following terms:

13, 23, 24, 25, 26

Here also,
`n=5`. So, the third term is the median.

∴ Q1 = 24

The second part has the following terms:

37, 47, 47, 48, 50

Here also,
`n=5`. So, the third term is the median.

∴ Q2 = 47.

Now, IQR = Q2 - Q1 = 47 - 24 = 23.